In particular, the paper is organized as follows. Firstly, we fix conventions and briefly review some of the basic elements of non-Riemannian geometry and the physics of Metric-Affine gravity. We then consider an extended version of the \(F(R,T,Q,{\cal T},{\cal D})\)  theory [1]}. To be more specific, working in a Metric-Affine setup, we consider the class of theories with gravitational Lagrangians of the form \(F(R,T,Q,{\cal T},{\cal D})\) , where \({\cal D}\)  is the divergence of the dilation current, the new add-on we are establishing here. Then, we obtain the field equations for this family of theories by varying with respect to the metric and the independent affine connection. Considering a linear function \(F\)  we then present a cosmological application for this model and finally switching off non-metricity and considering a scalar field coupled to torsion we obtain the modified Friedmann equations and also provide solutions for this simple case.
